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Unsteady lift for the Wagner problem in the presence of additional leading/trailing edge vortices. (English) Zbl 1337.74015
Summary: This study amends the inviscid Wagner lift model for starting flow at relatively large angles of attack to account for the influence of additional leading edge and trailing edge vortices. Two methods are provided for starting flow of a flat plate. The first method is a modified Wagner function, which assumes a planar trajectory of the trailing edge vortex sheet accounting for a temporal offset from the original Wagner function given release of leading edge vortices and a concentrated starting point vortex at the initiation of motion. The second method idealizes the trailing edge sheet as a series of discrete vortices released sequentially. The models presented are shown to be in good agreement with high-fidelity simulations. Through the present theory, a vortex force line map is generated, which clearly indicates lift enhancing and reducing directions and, when coupled with streamlines, allows one to qualitatively interpret the effect of the sign and position of vortices on the lift and to identify the origins of lift oscillations and peaks. It is concluded that leading edge vortices close to the leading edge elevate the Wagner lift curve while a strong leading edge vortex convected to the trailing edge is detrimental to lift production by inducing a strong trailing edge vortex moving in the lift reducing direction. The vortex force line map can be employed to understand the effect of the different vortices in other situations and may be used to improve vortex control to enhance or reduce the lift.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D17 Viscous vortex flows
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References:
[1] DOI: 10.1242/jeb.01471 · doi:10.1242/jeb.01471
[2] DOI: 10.1017/jfm.2013.28 · Zbl 1284.76059 · doi:10.1017/jfm.2013.28
[3] DOI: 10.1242/jeb.00848 · doi:10.1242/jeb.00848
[4] Fung, An Introduction to the Theory of Aeroelasticity (2002)
[5] DOI: 10.1038/35089071 · doi:10.1038/35089071
[6] DOI: 10.1038/384626a0 · doi:10.1038/384626a0
[7] DOI: 10.1002/zamm.19250050103 · JFM 51.0675.05 · doi:10.1002/zamm.19250050103
[8] DOI: 10.1016/j.cja.2013.07.022 · doi:10.1016/j.cja.2013.07.022
[9] Eames, J. Fluid Mech. 589 pp 33– (2008)
[10] DOI: 10.2514/3.12621 · Zbl 0824.76009 · doi:10.2514/3.12621
[11] DOI: 10.1016/j.cja.2014.03.014 · doi:10.1016/j.cja.2014.03.014
[12] Dickinson, J. Expl Biol. 174 pp 45– (1993)
[13] DOI: 10.1098/rspa.2011.0617 · Zbl 1364.76023 · doi:10.1098/rspa.2011.0617
[14] Ansari, J. Aerosp. Engng 220 pp 169– (2006)
[15] DOI: 10.1146/annurev.fl.17.010185.002211 · doi:10.1146/annurev.fl.17.010185.002211
[16] Saffman, Stud. Appl. Maths 57 pp 107– (1977) · Zbl 0385.76033 · doi:10.1002/sapm1977572107
[17] Ansari, J. Aerosp. Engng 220 pp 61– (2006)
[18] DOI: 10.1017/S0022112073001187 · Zbl 0255.76024 · doi:10.1017/S0022112073001187
[19] Saffman, Vortex Dynamics (1992)
[20] Anderson, Fundamentals of Aerodynamics (McGraw-Hill Series in Aeronautical and Aerospace Engineering) (2010)
[21] DOI: 10.2514/3.8967 · doi:10.2514/3.8967
[22] DOI: 10.2514/3.46467 · doi:10.2514/3.46467
[23] DOI: 10.1017/S002211208200113X · Zbl 0508.76028 · doi:10.1017/S002211208200113X
[24] DOI: 10.2514/8.3180 · doi:10.2514/8.3180
[25] DOI: 10.1017/S0022112004008821 · Zbl 1163.76329 · doi:10.1017/S0022112004008821
[26] DOI: 10.1017/S0022112078002189 · Zbl 0393.76018 · doi:10.1017/S0022112078002189
[27] DOI: 10.1007/s00348-009-0631-8 · doi:10.1007/s00348-009-0631-8
[28] DOI: 10.1098/rsbl.2012.0130 · doi:10.1098/rsbl.2012.0130
[29] DOI: 10.1126/science.1153019 · doi:10.1126/science.1153019
[30] DOI: 10.1103/PhysRevE.66.051907 · doi:10.1103/PhysRevE.66.051907
[31] Milne-Thomson, Theoretical Hydrodynamics (1968) · doi:10.1007/978-1-349-00517-8
[32] DOI: 10.1007/s00162-009-0117-6 · Zbl 1191.76074 · doi:10.1007/s00162-009-0117-6
[33] DOI: 10.1016/j.jfluidstructs.2009.06.002 · doi:10.1016/j.jfluidstructs.2009.06.002
[34] DOI: 10.1242/jeb.02614 · doi:10.1242/jeb.02614
[35] Li, Trans. ASME: J. Fluids Engng 137 (2015)
[36] DOI: 10.1126/science.1174196 · doi:10.1126/science.1174196
[37] DOI: 10.1242/jeb.022269 · doi:10.1242/jeb.022269
[38] DOI: 10.2514/3.10746 · doi:10.2514/3.10746
[39] Knowles, Proceedings of the 3rd International Symposium on Integrating CFD and Experiments in Aerodynamics, 20–21 June 2007. U.S. Air Force Academy (2007)
[40] DOI: 10.1017/S0022112008000359 · Zbl 1151.76493 · doi:10.1017/S0022112008000359
[41] DOI: 10.1007/BF02484543 · doi:10.1007/BF02484543
[42] Johansson, Nat. Sci. Rep. 3 pp 3264– (2013)
[43] DOI: 10.1063/1.4819878 · Zbl 06480171 · doi:10.1063/1.4819878
[44] DOI: 10.1016/0021-9991(86)90099-9 · Zbl 0619.76024 · doi:10.1016/0021-9991(86)90099-9
[45] DOI: 10.1017/jfm.2012.45 · Zbl 1250.76029 · doi:10.1017/jfm.2012.45
[46] DOI: 10.2514/3.7913 · Zbl 0479.76018 · doi:10.2514/3.7913
[47] DOI: 10.2514/3.50966 · Zbl 0461.76041 · doi:10.2514/3.50966
[48] DOI: 10.1093/qjmam/48.3.401 · Zbl 0836.76028 · doi:10.1093/qjmam/48.3.401
[49] DOI: 10.1017/jfm.2014.18 · doi:10.1017/jfm.2014.18
[50] DOI: 10.1017/S0022112083001986 · Zbl 0524.76016 · doi:10.1017/S0022112083001986
[51] DOI: 10.1017/jfm.2012.368 · Zbl 1275.76232 · doi:10.1017/jfm.2012.368
[52] DOI: 10.1017/S0022112010000613 · Zbl 1193.76031 · doi:10.1017/S0022112010000613
[53] DOI: 10.1017/S0022112080002595 · doi:10.1017/S0022112080002595
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